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If today is Monday we know that in 702 days time (that is in 100 weeks and 2 days time) it will be Wednesday. This is an example of "clock" or "modular" arithmetic.
What day will it be in 15 days? 26 days? 234 days?
In 2, 9, 16 and 23 days from now, it will be a Wednesday.
What other numbers of days from now will be Wednesdays?
Can you generalise what you have noticed?
Choose a pair of numbers and find the remainders when you divide by 7.
Then find the remainder when you divide the total by 7. For example:
$15 \div 7 = 2$ remainder $1$ | $15 + 26 = 41$ | |
$26 \div 7 = 3$ remainder $5$ | $41 \div 7 = 5$ remainder $6$ |
Choose some more pairs of numbers.
Is there a relationship between the remainders when you divide each by 7, and the remainder when you divide their total by 7?
Now find the remainder when you divide the product of 15 and 26 by 7. What happens?
Choose some more pairs of numbers.
Is there a relationship between the remainders when you divide each by 7, and the remainder when you divide their product by 7?